(A) Factor: 8x²-2xy-1y² 

Multiply the 8 by the 1 ignoring signs.  Get 8

Write down all the ways to have two positive integers
which have product 8, starting with 8*1

8*1
4*2


Since the last sign in 8x²-2xy-1y² is -, SUBTRACT them,
and place the DIFFERENCE out beside that:

8*1   8-1=7
4*2   4-2=2

Now, again ignoring signs, we find in that list of
differences the coefficient of the middle term in 8x²-2xy-1y²

So we replace the number 2 by 4-2

8x²-2xy-1y²
8x²-(4-2)xy-1y²

Then we distribute to remove the parentheses:

8x²-4xy+2xy-1y²

Factor the first two terms 8x²-4xy by taking out the
greatest common factor, 4x, getting 4x(2x-y)

Factor the last two terms +5x-10 by taking out the
greatest common factor y, getting +y(2x-y)

So we have4
4x(2x-y)+y(2x-y)

Notice that there is a common factor, (2x-y)

4x(2x-y)+y(2x-y)

which we can factor out leaving the 4x and the +y to put 
in parentheses:

(2x-y)(4x+y)

Edwin